I doubt I'd squeeze any more accuracy out of the rifle
Why would you think that? It's a rifle isn't it. It may be just an SKS, but, handloading could help. You could try a host of different bullets from .308 to .312 , hell, you might even find a bullet that that SKS really likes. If not, then no harm done, just nice little journey down the road to better accuracy that ended up a dead end.
I handload for my Ruger Mini-30 and I have found some very very accurate loads and some very bad ones as well.
Give it a try, what to you have to lose except some bench time and some range time.